There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.


Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11


Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.

The function g is defined by:

g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1.

The random variable X = g(U) has the exponential (lambda) distribution.

(i) To create a random variable X that has cdf F, and you have a number picked uniformly on (0,1), you should do the following:

Let U be a uniform (0,1) random variable. To construct a random variable X=F^(-1)(U) so that X has the cdf F, take the inverse of the cdf F, denoted as F^(-1), and apply it to the uniformly distributed random variable U.

(ii) To find the function g for an exponential distribution with parameter lambda, you should set F as the exponential cdf, which is given by:

F(x) = 1 - e^(-lambda * x)

Now, you can find the inverse function F^(-1)(u):

1. Set u = F(x): u = 1 - e^(-lambda * x)
2. Solve for x: x = - (1/lambda) * ln(1 - u)

So, the function g is defined by g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1. The random variable X = g(U) has the exponential (lambda) distribution.

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Answer:

Step-by-step explanation:

The factors of 12 and 15 common number is 3. You can do rows of 3 four times to get 12 rose bushes and rows of 3, five times to get 15 tulips.
4x3 = 12  and 5x3 = 15. This is how I understood the question.

Answer:

3

Step-by-step explanation:

the factors of 12 are

1,2,3,4,6,12

and the factors of 15 are

1,3,5,15

so the answer would be 3

( i did the quiz and got it right )

The probability P(A and B)  that both events will occur is 8/13

From the question, we have the following parameters that can be used in our computation:

Event A = 6 and 6

Event B = 20 and 6

Event A and B = 6

Total = 6 + 6 + 20 + 6 - 6 + 20 = 52

Using the above as a guide, we have the following:

P(A) = 12/52

P(B) = 26/52

P(A and B) = 6/52

The probability that both events will occur is represented as

P(A and B) = P(A) + P(B) - P(A and B)

And this is calculated as

P(A and B) = P(A) + P(B) - P(A and B)

Substitute the known values in the above equation, so, we have the following representation

P(A and B) = 12/52 + 26/52 - 6/52

Evaluate

P(A and B) = 32/52

Simplify

P(A and B) = 8/13

Hence, the probability that both events will occur is 8/13

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Answer:

first problem: 1,2,4

second problem: D

Step-by-step explanation:

Answer:

20.40 ft

Step-by-step explanation:

a^2 + b^2 = c^2 (right triangle) (sides of the triangle are the house and the distance from the base of the ladder to the house. The hypotenuse is the ladder.

20^2 + 4^2 = c^2

400 + 16 = c^2

C = sqrt 416

C = 20.40 ft

Answer: False

(5 x 3) + (5 x 3) = 30

Answer: I believe the correct answer is the last one but I’m not entirely sure, wait for someone else to answer.

Step-by-step explanation:

Answer:

third one

Step-by-step explanation:

point-slope form is y - y1 = m(x - x1)

plug in values  y -(-5) = 2/3(x - 4)

the double negative cancels out and becomes a positive

therefore y + 5 = 2/3(x - 4)

Step-by-step explanation:

by the way, you are completely and exactly right at 6.

Q is the inscribed angle of the (inner) arc angle TR.

and as such it is half of that arc angle TR.

S is now on the same side of the circle center as the segment TR. so, we have to flip the situation around :

S is half of the outside arc angle between T and R.

as the sum of the inner and outside arc angles are 360° (the full circle), the sum of half of their values is then

360/2 = 180°

so, yes,

x + 2 + 9x - 7 = 180

10x - 5 = 180

10x = 185

x = 18.5

Q = x + 2 = 18.5 + 2 = 20.5°

S = 9x - 7 = 9×18.5 - 7 = 166.5 - 7 = 159.5°

(a) The density of |x| is 1/2 for 0 ≤ |x| ≤ 1.

(b) The density of p|x| is 1/(2p) for p > 0.

(c) The density of -ln|x| is 1/(2e^y) for y < 0.

(d) The density of sin(x) is (1/2) * |cos(x)|.

(a) To find the density of |x|, we need to consider the probability distribution of |x|. Since x is uniformly distributed on the interval (-1, 1), its probability density function (pdf) is constant within this interval and zero outside it. We know that |x| is non-negative and will take values between 0 and 1.

To determine the density of |x|, we can calculate the cumulative distribution function (CDF) of |x| and then differentiate it to obtain the pdf.

The CDF of |x| can be expressed as P(|x| ≤ t) where t is a value between 0 and 1. Since x is uniformly distributed, P(|x| ≤ t) is equal to the length of the interval (-t, t) divided by the length of the interval (-1, 1), which is 2.

Therefore, the CDF of |x| is given by F(t) = t/2 for 0 ≤ t ≤ 1.

Differentiating the CDF, we get the pdf of |x|:

f(t) = dF(t)/dt = 1/2 for 0 ≤ t ≤ 1.

(b) To find the density of p|x|, we can apply the transformation rule for probability densities. Since p is a constant, the density of p|x| is given by:

f(p|x|) = (1/2) * (1/p) = 1/(2p) for p > 0.

(c) To find the density of\(-ln|x|\), we apply the transformation rule again. Let y = -ln|x|. Solving for x, we have \(x = e^(-y)\). Taking the derivative of this transformation, we get \(dx/dy = -e^(-y)\).

Since |x| = e^(-y) and dx/dy = \(-e^(-y)\), we have:

\(f(-ln|x|) = f(y) = (1/2) * |-e^(-y)| = 1/(2e^y) for y < 0.\)

(d) To find the density of sin(x), we consider the transformation y = sin(x). The derivative of this transformation is dy/dx = cos(x).

Since sin(x) = y and dy/dx = cos(x), we have:

f(sin(x)) = f(y) = (1/2) * |cos(x)|.

Note that the absolute value is used here because cos(x) can be positive or negative depending on the value of x.

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Answer:

About 7.07% of the visitors bought a gift.

Step-by-step explanation:

7/99 = 0.0707

0.0707 *100 = 7.07%

then:

About 7.07% of the visitors bought a gift.

Answer:

250 ft

Step-by-step explanation:

circumference of a circle = πD

D = diameter

to find diameter divide by pi

d = 250

Answer:

−1 < x < 4

Hoped this helped ⊂◉‿◉つ

Answer:

x = ±2

Step-by-step explanation:

Move the 3 to the left side of the equation by subtracting it. This way, you get:

2=|x|.

Because x is an absolute value, that means the value of x can be negative or positive. That is why there is a "±" symbol beside the 2 in the answer.

The length of q is 7.5 that is nearest 10th of a centimeter.

Given that,

In ΔOPQ, p is 7. 2 cm, ∠P is 36° and ∠Q is 38°.

To find : To the closest 10th of a centimeter, the length of q

Three sides (a, b, c) and three angles (,, ) make up each triangle's six essential qualities. The standard trigonometry challenge is to identify three of these six features and then determine the remaining three. Of course, our triangle solver uses combinations of basic and derived characteristics, including area, perimeter, heights, medians, and so forth. Usually by side-angle-side (SSS), side-side-angle (SSA), or length of three sides (L3).

The length of q is therefore 7.5, or to the nearest tenth of a centimeter.

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The solution of the system is x = 4 and y = 1.

To solve the system of equations using the elimination method, we can eliminate one variable by adding or subtracting the equations.

In this case, we can eliminate the variable "x" by multiplying the first equation by -2 and adding it to the second equation.

1. Multiply the first equation by -2:

  -8x - 4y = -36

2. Add the modified first equation to the second equation:

  -8x - 4y + 2x + 3y = -36 + 15

Simplifying the equation gives:

  -6x - y = -21

3. Solve the new equation for one variable. Let's solve for y:

  -y = -21 + 6x

   y = 21 - 6x

4. Substitute the value of y into one of the original equations. Let's use the first equation:

  4x + 2(21 - 6x) = 18

Simplifying the equation gives:

  4x + 42 - 12x = 18

  -8x = -24

   x = 3

5. Substitute the value of x back into the equation for y:

  y = 21 - 6(3)

  y = 21 - 18

  y = 3

Therefore, the solution to the system of equations is x = 3 and y = 3.

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Answer:

She writes the sum of the ten integers, then factors her expression. She correctly determines the total change for the 10 months.

Step-by-step explanation:

i might be right

Integer be x

\(\\ \rm\rightarrowtail 2x^2+6=12x\)

\(\\ \rm\rightarrowtail 2x^2-12x+6=0\)

Equation is

\(\\ \rm\rightarrowtail x^2-6x+3=0\)

Answer:

33 1/3%

Step-by-step explanation:

Explained in question comments :)

The percent of Mrs. Vega's class who wrote a 4 page book report is 33 1/3 %.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given a dot plot which shows the number of pages written by the students in her first-period class.

Total number of students in Mrs. Vega's class = 18

[Total number of students is the number of dots in the dot plot]

Number of students who wrote 4 pages = number of dots above 4 = 6

Percentage of students who wrote 4 pages = 6/18

                                                                         = 0.333

                                                                         = 33.3%

                                                                         = 33 1/3 %

Hence the required percent is 33 1/3 %.

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The Johan gets R1,200 of the R1,800 that was divided among the three people.

Let the amount of money that Pierre gets be p.Then Mark will get 2p and Johan will get 3(2p) = 6p

Since the total amount of money is R1,800, we have:p + 2p + 6p = 1800Simplifying,

we get:

9p = 1800Dividing both sides by 9,

we get:p = 200

Therefore, Mark gets 2p = 2(200) = 400 and Johan gets 6p = 6(200) = 1200

Therefore, Johan gets R1,200 of the R1,800 that was divided among the three people.

Another way of approaching the problem is to use ratios. If we let the ratio of amounts that Pierre, Mark, and Johan get be x, y, and z respectively,

then we have:x + y + z = 1 (since the total amount is 1)z = 3y (since Johan gets three times as much as Mark)y = 2x (since Mark gets twice as much as Pierre)Substituting the second and third equations into the first, we get:x + 2x + 6x = 1

Simplifying, we get:9x = 1Dividing both sides by 9,

we get:x = 1/9

Therefore, y = 2x = 2/9 and z = 3y = 6/9 = 2/3

Since R1,800 was divided among the three people, Johan gets:z × 1800 = (2/3) × 1800 = 1200

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Answer:.

Step-by-step explanation:

Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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The Temperature in Kelvin is 293.15 K.

To convert temperature from degrees Celsius (°C) to Kelvin (K), you can use the following formula:

Temperature in Kelvin = Temperature in Celsius + 273.15

Given that the room temperature is measured at 20.0 °C, we can calculate the temperature in Kelvin as follows:

Temperature in Kelvin = 20.0 °C + 273.15

Temperature in Kelvin = 293.15 K

Therefore, the temperature in Kelvin is 293.15 K.

The Kelvin scale is an absolute temperature scale where 0 K represents absolute zero, the point at which all molecular motion ceases. The Kelvin scale is widely used in scientific and engineering applications, especially in situations where precise temperature measurements and calculations are necessary.

It's important to note that the Kelvin scale does not use the degree symbol (°) when denoting temperature. Instead, temperatures are simply expressed in Kelvins (K) as a unit of measurement.

Converting temperatures between Celsius and Kelvin is a simple process and involves adding or subtracting the appropriate value (273.15) to or from the temperature in Celsius. This conversion is useful in many scientific calculations and ensures consistency and accuracy when working with temperature data.

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Answer:

293.15 K.

Step-by-step explanation:

The solution to the equation does not exist

From the question, we have the following parameters that can be used in our computation:

2x - 3 = 0

2x - 3 = 3

Also from the question, we understand that the graph is given as

3 = 0

The above equation is false, and cannot be represented on a graph

This is so because 0 and 3 do not have the same value

Similarly, we have 2x - 3 = 0 and 2x - 3 = 3

By substitution, the equations becomes

0 = 3

Hence, the equation has no solution

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Complete question

Graph of 3=0

Solve the equation 2x - 3 = 0 and 2x - 3 = 3 graphically

Answer:

2hours  = 13 games 12 divided by 2

 13

x 6

--------

78

joseph plays 78 matches of among us a day

The store's markup on the tablet is equal to $350. Hence, option D is correct.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the information in the question,

Don bought a new tablet.

The cost of buying a tablet for Don = $550

The cost at which the store is buying the tablet = $200

Then, the markup on the tablet will be,

= 550 - 200

= $350

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Answer: d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the equation 25^(z − 4) = 125, this can also be written as;

\(5^{2(z-4)} = 5^3\\2(z-4) = 3\\2z - 8 = 3\\2z = 3+8\\2z = 11\\z = 11/2\\z = 5.5\)

Hence the value of z is 5.5

Answer:

z=3.5

Step-by-step explanation:

I took the test and got it right

Answer:

13

Step-by-step explanation:

Since Seth pays $0.50 for each check he writes, he would write (let x be how many checks Seth wrote) "x" checks for $6.50. That means;

1 = 0.50

x = 6.50

Now let us set up a fraction:

\(\frac{0.5}{1}=\frac{6.5}{x}\)

Step 1: Cross multiply

\(0.5x=1\cdot \:6.5\)

\(0.5x=6.5\)

Step 2: Divide both sides by \(0.5\)

\(\frac{0.5x}{0.5}=\frac{6.5}{0.5}\)

Simplify

\(x=13\)

Therefore, Seth will write 13 checks for $6.50

Barton should use a luggage scale to get the most accurate and appropriate measurement of his packed suitcase before he leaves to catch a flight. A luggage scale is a compact and portable device that is designed specifically to weigh luggage. Using a luggage scale is easy and convenient as it allows travelers to weigh their bags accurately, ensuring that they are within the airline's weight limit. To use a luggage scale, Barton should follow these simple steps:

Step 1: Attach the luggage strap Barton should attach the luggage strap to the handle of his suitcase.The strap should be attached in such a way that it can support the weight of the suitcase without slipping or coming off.

Step 2: Turn on the luggage scale Barton should turn on the luggage scale and wait for it to calibrate. This usually takes a few seconds. Once the scale is calibrated, it will display a zero reading.

Step 3: Lift the suitcase Barton should lift the suitcase by the luggage strap until it is off the ground. The luggage scale will display the weight of the suitcase on its digital display. This reading is the weight of the suitcase including all the contents inside.

Step 4: Check the weight If the weight of the suitcase is less than 50 pounds, Barton can go ahead and catch his flight without worrying about any extra charges. If the weight of the suitcase is more than 50 pounds, Barton will have to remove some items from the suitcase or pay the extra fee charged by the airline.

Therefore, using a luggage scale is the most accurate and appropriate method for travelers like Barton to measure their suitcase weight before boarding their flight.

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Answer:

use a standard digital bathroom scale.

Step-by-step explanation: